The strongly interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [S. Vuckovic and P. Gori-Giorgi, J. Phys. Chem. Lett. 8, 2799–2805 (2017)] introduced the “multiple radii functional” (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyze the MRF in exactly solvable one-dimensional molecules to uncover how it matches and deviates from exact results and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. We show that range-separated treatment of the MRF can offer advantages over a full treatment, by using MRF for short-ranged and/or midranged interactions only. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.